Periodicity conjecture for the heuristic APD-algorithm on cubic conjugate vectors

A cubic conjugate vector is a vector arising from a cubic algebraic number together with its conjugates, as in the paper's definition; a triple of cubic conjugate vectors is a triple of such vectors associated with the three conjugate roots of an irreducible cubic polynomial. The heuristic APD-algorithm is an algorithm applied to such triples.

Periodicity conjecture. The heuristic APD-algorithm is periodic for all triples of cubic conjugate vectors.

The preceding example exhibits eventual periodicity for a particular triple, but the claim asserts periodicity for every triple of cubic conjugate vectors. The parser supplies no evidence that this conjecture has been resolved.